Information on Result #657220
Linear OA(258, 31, F25, 6) (dual of [31, 23, 7]-code), using construction X applied to AG(F, Q+5P) ⊂ AG(F, Q+6P) based on
- linear OA(256, 26, F25, 6) (dual of [26, 20, 7]-code or 26-arc in PG(5,25)), using algebraic-geometric code AG(F, Q+8P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
- linear OA(253, 26, F25, 3) (dual of [26, 23, 4]-code or 26-arc in PG(2,25) or 26-cap in PG(2,25)), using algebraic-geometric code AG(F, Q+6P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(252, 5, F25, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(2533, 657, F25, 13) (dual of [657, 624, 14]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2545, 15657, F25, 13) (dual of [15657, 15612, 14]-code) | [i] | ||
| 3 | Linear OA(2557, 390657, F25, 13) (dual of [390657, 390600, 14]-code) | [i] | ||
| 4 | Linear OA(2531, 656, F25, 12) (dual of [656, 625, 13]-code) | [i] | ||
| 5 | Linear OA(2542, 15656, F25, 12) (dual of [15656, 15614, 13]-code) | [i] | ||
| 6 | Linear OA(2553, 390656, F25, 12) (dual of [390656, 390603, 13]-code) | [i] | ||
| 7 | Linear OA(2533, 659, F25, 13) (dual of [659, 626, 14]-code) | [i] | ||
| 8 | Linear OA(2545, 15659, F25, 13) (dual of [15659, 15614, 14]-code) | [i] | ||
| 9 | Linear OA(2557, 390660, F25, 13) (dual of [390660, 390603, 14]-code) | [i] | ||
| 10 | Linear OA(2531, 659, F25, 12) (dual of [659, 628, 13]-code) | [i] | ||
| 11 | Linear OA(2542, 15659, F25, 12) (dual of [15659, 15617, 13]-code) | [i] | ||
| 12 | Linear OA(2553, 390660, F25, 12) (dual of [390660, 390607, 13]-code) | [i] | ||
| 13 | Linear OA(25105, 15657, F25, 32) (dual of [15657, 15552, 33]-code) | [i] | Construction X with Cyclic Codes | |
| 14 | Linear OA(2599, 15657, F25, 30) (dual of [15657, 15558, 31]-code) | [i] | ||
| 15 | Linear OA(2593, 15657, F25, 28) (dual of [15657, 15564, 29]-code) | [i] | ||
| 16 | Linear OA(2587, 15657, F25, 26) (dual of [15657, 15570, 27]-code) | [i] | ||
| 17 | Linear OA(2581, 15657, F25, 24) (dual of [15657, 15576, 25]-code) | [i] | ||
| 18 | Linear OA(2575, 15657, F25, 22) (dual of [15657, 15582, 23]-code) | [i] | ||
| 19 | Linear OA(2569, 15657, F25, 20) (dual of [15657, 15588, 21]-code) | [i] | ||
| 20 | Linear OA(2563, 15657, F25, 18) (dual of [15657, 15594, 19]-code) | [i] | ||
| 21 | Linear OA(25109, 390656, F25, 27) (dual of [390656, 390547, 28]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 22 | Linear OA(25105, 390656, F25, 26) (dual of [390656, 390551, 27]-code) | [i] | ||